• Communications of the Korean Mathematical Society
• /
• v.30 no.4
• /
• pp.429-438
• /
• 2015

In this paper, we discuss how the operational calculus can be exploited to the theory of mixed generating functions. We use operational methods associated with multi-variable Hermite polynomials, Laguerre polynomials and Bessels functions to drive identities useful in electromagnetism, fluid mechanics etc. Certain special cases giving bilateral generating relations related to these special functions are also discussed.

• Communications for Statistical Applications and Methods
• /
• v.15 no.6
• /
• pp.837-842
• /
• 2008

Students taking linear model courses have difficulty in determining which parametric functions are estimable when the design matrix of a linear model is rank deficient. In this note a special form of estimable functions is presented with a linear combination of some orthogonal estimable functions. Here, the orthogonality means the least squares estimators of the estimable functions are uncorrelated and have the same variance. The number of the orthogonal estimable functions composing the special form is equal to the rank of the design matrix. The orthogonal estimable functions can be easily obtained through the singular value decomposition of the design matrix.

• Journal of Information Technology Services
• /
• v.13 no.3
• /
• pp.111-128
• /
• 2014

President Park Geun-hye Administration has established the Ministry of Science, ICT and Future Planning (MSIP) to build a creative economy using Information and Communication Technology (ICT). July 2, 2013, The National Assembly has legislated the special act on the ICT promotion and convergence so called special ICT Act. This special ICT Act has reduced the legal basis through legislative process and departmental agreement. Therefore many experts worried that since the MSIP's key functions and roles are being reduced, there will be a limit to the MSIP's endeavor for the advancement of science technology and the ICT promotion and convergence. The establishment of the Agency, together with the formation of 'IT Strategy Committee', is considered to be one of the core items of the Special Act on ICT. MSIP originally planned to integrate the ICT R&D functions scattered across many governmental organizations, including Korea Communications Agency (KCA), KEIT and Korea Creative Contents Agency (KOCCA), into the Agency to separate the national ICT R&D from private R&D and streamline the process of 'discovery-selection-evaluation-commercialization'. The analytical results in this study are supposed to the establishment of efficient ICT governance systems as the practical strategies to actively cope with the changes of ICT convergence environment. It is also expected to the revision on the special ICT Act in the ICT budget and governance. Therefore, MSIP should cover research and development (R&D) as well as major ICT promotion functions to a creative economy.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.3
• /
• pp.831-845
• /
• 2014

In this paper, we obtain new generating functions involving families of pairs of inverse functions by using a generalization of the Srivastava's theorem [H. M. Srivastava, Some generalizations of Carlitz's theorem, Pacific J. Math. 85 (1979), 471-477] obtained by Tremblay and Fug$\grave{e}$ere [Generating functions related to pairs of inverse functions, Transform methods and special functions, Varna '96, Bulgarian Acad. Sci., Sofia (1998), 484-495]. Special cases are given. These can be seen as generalizations of the generalized Bernoulli polynomials and the generalized degenerate Bernoulli polynomials.

• Kyungpook Mathematical Journal
• /
• v.45 no.2
• /
• pp.153-159
• /
• 2005

In the present paper, we obtain two Theorems connecting the unified fractional integral operators and the Laplace transform. Due to the presence of a general class of polynomials, the multivariable H-function and general functions ${\theta}$ and ${\phi}$ in the kernels of our operators, a large number of (new and known) interesting results involving simpler polynomials (which are special cases of a general class of polynomials) and special functions involving one or more variables (which are particular cases of the multivariable H-function) obtained by several authors and hitherto lying scattered in the literature follow as special cases of our findings. Thus the Theorems obtained by Srivastava et al. [9] follow as simple special cases of our findings.

• Kyungpook Mathematical Journal
• /
• v.46 no.1
• /
• pp.49-56
• /
• 2006

The aim of the present work is to obtain the inverse Laplace transform of the product of the factors of the type $s^{-\rho}\prod\limit_{i=1}^{\tau}(s^{li}+{\alpha}_i)^{-{\sigma}i}$, a general class of polynomials an the multivariable H-function. The polynomials and the functions involved in our main formula as well as their arguments are quite general in nature. On account of the general nature of our main findings, the inverse Laplace transform of the product of a large variety of polynomials and numerous simple special functions involving one or more variables can be obtained as simple special cases of our main result. We give here exact references to the results of seven research papers that follow as simple special cases of our main result.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.5
• /
• pp.1007-1014
• /
• 2012

We derive the exact reciprocity formula connecting the twisted second moments at 1 for families of odd Dirichlet characters corresponding to two prime moduli, which parallels such formula discovered earlier for the special point 1/2.

• Korean Journal of Mathematics
• /
• v.27 no.4
• /
• pp.899-927
• /
• 2019

In this paper we establish some results depending on the comparative growth properties of composite entire and meromorphic functions using relative (p, q)-th order and relative (p, q)-th lower order where p, q are any two positive integers and that of a special type of differential polynomial generated by one of the factors.

• Communications of the Korean Mathematical Society
• /
• v.37 no.1
• /
• pp.207-212
• /
• 2022

In this paper, an interesting integral involving the Ī-function of one variable introduced by Rathie has been derived. Since Ī-function is a very generalized function of one variable and includes as special cases many of the known functions appearing in the literature, a number of integrals can be obtained by reducing the Ī function of one variable to simpler special functions by suitably specializing the parameters. A few special cases of our main results are also discussed.

• Honam Mathematical Journal
• /
• v.39 no.3
• /
• pp.443-451
• /
• 2017

Very recently, Agarwal gave remakably a scads of fractional integral formulas involving various special functions. Using the same technique, we obtain certain(presumably) new fractional integral formulas involving the product of confluent hypergeometric functions. Some interesting special cases of our two main results are considered.